Find the interior int (S), the boundary bd (S), the closure cl (S), and the set

Question

Find the interior int (S), the boundary bd (S), the closure cl (S), and the set accumulation points S' of each subset S of R.

Classify the set S as open, closed, neither, or both. Is S a compact set? Justify your answers.

For each subset S of R, find its supremum sup S, maximum max S, infimum inf S, and minimum min S, if exists. Otherwise, write "DNE". Justify your answers.

a. S = { (-1)^n + (-1)^n/n | n is an element of N }

b. S = U [ -2+1/(n^2), 2-1(2n+1) ] when n is an element of N

c. S = nQ {pi}

d. S = { x is an element of R | 0 < x^2 <= 3 }

please answer any of the following questions, if not all.

Explanation / Answer

a.)

S = { (-1)^n + (-1)^n/n | n is an element of N }

S = { -2 , 1.5 , -1.33 , 1.25 , -1.2 , ...... 1}

sup S = 1

max= DNE

min = DNE

d ) S = { x is an element of R | 0 < x^2 <= 3 }

min = -(3)^0.5

max = +3^0.5

SUP = DNE

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